Generalized context-free grammar

Generalized Context-free Grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context free composition functions to rewrite rules.Head grammar (and its weak equivalents) is an instance of such a GCFG which is known to be especially adept at handling a wide variety of non-CF properties of natural language.

A GCFG consists of two components: a set of composition functions that combine string tuples, and a set of rewrite rules. The composition functions all have the form ${\displaystyle f(\langle x_{1},...,x_{m}\rangle ,\langle y_{1},...,y_{n}\rangle ,...)=\gamma }$, where ${\displaystyle \gamma }$ is either a single string tuple, or some use of a (potentially different) composition function which reduces to a string tuple. Rewrite rules look like ${\displaystyle X\to f(Y,Z,...)}$, where ${\displaystyle Y}$, ${\displaystyle Z}$, ... are string tuples or non-terminal symbols.

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